Burnham was picked in the 22nd round of the 1993 amateur draft out of high school by the Chicago Cubs. He opted for college instead and would play for four seasons for Clemson. In 1994, he hit .277 in 47 AB for the #4 team in NCAA Division I. In 1995, the sophomore outfielder batted .344 with a team-high 27 doubles for the #6 team in NCAA Division I; he had a better average than teammate Matt LeCroy and was named 3rd-team All-American by the BBWA. During the 1996 campaign, Gary hit .290 with a team-high 24 doubles and 62 runs, tied for the club lead, as Clemson finished 5th. The Oakland A's chose Burnham in the 40th round of the 1996 amateur draft; again, he did not sign. During his summer months, Burnham played in the Cape Cod Baseball League for Orleans in '95 and Falmouth in '96. He made the all star team both years and was awarded MVP of the 95 all star game. Returning for a senior season, the South Windsor native batted .391, tied for 5th in the Atlantic Coast Conference. He had 23 doubles, 15 home runs, 83 runs and 82 RBI. He failed to make All-ACC despite his fine hitting. He was chosen by the Philadelphia Phillies in the 22nd round of the 1997 amateur draft and signed.

Burnham made his pro debut with the Batavia Clippers and batted .325/~.389/.481 with 22 doubles in 289 AB. He was second in the New York-Penn League in batting average and 5th in doubles. He made the league All-Star team at DH. Gary was promoted to the Clearwater Phillies for 1998 and hit .296/~.373/.446 with 33 doubles, 10 triples and 93 runs. He led Florida State League first basemen with a .994 fielding percentage. He led his team in runs and triples.

In 1999, the left-handed hitter took his cuts for the Reading Phillies, resulting in a .249/~.340/.407 in 116 games, splitting time between first base and the outfield. The next season, Burnham batted .268/.363/.456 with 28 doubles for Reading. During 2001, Gary had a third season with Reading and hit .318/.385/.518 with 25 doubles and 15 homers. He had the best average in the Phillies farm system. Burnham was third in the Eastern League in average behind Dustan Mohr and Marcus Thames and right ahead of teammate Marlon Byrd. He also led the EL with 9 sacrifice flies. Eric Munson beat him out for EL All-Star honors at first base.

Burnham was traded to the Toronto Blue Jays during spring training 2002. They gave the 27-year-old his first look at AAA with the 2002 Syracuse SkyChiefs; he hit .281/.363/.443 with 34 doubles, 17 home runs and 88 RBI. He was awarded team MVP. He led Syracuse in RBI and tied Simon Pond for the most RBI in the Toronto farm chain. He also led Jays minor leaguers in total bases (238). He was third in the International League in RBI, behind Kevin Witt and David Doster and led league first basemen with 91 assists. He ground into 19 double plays, tying Johnny Estrada for the high (or low, depending on your meaning) mark in the circuit. He hit 6th in the 2002 AAA All-Star Game, going 0 for 2 for the IL before exiting in a 5-0 loss.

In 2003, Burnham remained in the wings in case anything happened to Carlos Delgado. He hit .269/.328/.424 for Syracuse with just 9 home runs in an off-year.

In 2005, the 30-year-old Clemson alumnus played for the independent Bridgeport Bluefish, hitting .320 and slugging .523 with 84 RBI. He led his team in runs (75), doubles (32), home runs (18) and RBI. He finished second in the circuit in average, .009 behind Carlos Hernandez. That earned him All-Star outfield honors and team MVP award.

After starting 2006 well with Bridgeport, Burnham returned to the Phillies system on May 23, 2006. He hit .341/.412/.576 in 80 games for Reading, with 16 homers and 60 RBI and batted .391/.429/.565 with 9 runs and 8 RBI in 10 games for the Scranton/Wilkes-Barre Red Barons. He still did not get a look from the majors, though Philadelphia had a pretty impressive first baseman in MVP Ryan Howard (58 HR, 149 RBI). Despite missing most of the first 2 months Burnham led Phillies farmhands in average (.343), home runs (17), and RBI (68) and set the Reading franchise record by hitting his 54th for them. He was recognized as a Topps national player of the month for his 10 homers in the month of August. Reading awarded him team MVP.

Burnham played DH, 1B and outfield for the 2007 Ottawa Lynx, hitting .292/.391/.436 with 35 doubles and 84 RBI despite only homering 12 times. His 84 RBI tied Shane Spencer for most RBIs ever recorded by an Ottawa Lynx in franchise history. He still led the team in doubles, homers and RBI and drew an IL-high 9 intentional walks. He led the 2007 International League in OBP, tied Joey Votto for 4th in the IL in walks (70), was only 6 doubles behind leader Brandon Moss. For his fine hitting the Ottawa Lynx named him their team MVP.

In 2010 the Reading Phillies named Gary Burnham to their All-Decade team as an outfielder.

In December 2008, Burnham inked a deal with the Chiba Lotte Marines of Japan. He was also put on Italy's preliminary roster for the 2009 World Baseball Classic but did not make the final cut choosing to stay in Japan for spring training. He debuted in Japan on April 4, going 0 for 2 after replacing Benny Agbayani at DH. He hit only .218/.348/.361 in 73 games in 2009.